Two-dimensional inverse scattering formula varying both frequency and incident angle using a circle as measurement surface

A reconstruction algorithm is described which combines the angular diversity and frequency diversity method. The two-dimensional scattering object is illuminated by a point source which is placed in the far field and successively occupies all positions on a circle surrounding the object. The input data is the scattered field measured at all positions on the circle and transformed into the far field. The reconstruction formula provides the object function within the Born approximation. Integration over receiver positions and all frequencies can be combined as one two-dimensional Fourier integral over the spatial frequency vector K. The result is integrated over all source positions. Because of varying the frequency and the observation point the K-space contains redundant information.